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Low carbon dioxide (CO2) emissions make nuclear energy crucial in decarbonizing the economy. In this context, nuclear safety, and especially the operation of nuclear power plants, remains a critical issue. This article presents a new fractal cluster method of control that improves the quality of assessing fuel element cladding integrity, which is critical for nuclear and environmental safety. The proposed non-destructive testing method allows for detecting defects on the inner and outer cladding surfaces without removing the elements from the nuclear reactor, which ensures prompt response and prevention of radiation leakage. Studies have shown that the fractal dimension of the cladding surface, which varies from 2.1 to 2.5, indicates significant heterogeneity caused by mechanical damage or corrosion, which can affect its integrity. The density analysis of defect clusters allows quantifying their concentration per unit area, which is an important indicator for assessing the risks associated with the operation of nuclear facilities. The data obtained are used to assess the impact of defects on the vessel’s integrity and, in turn, on nuclear safety. The monitoring results are transmitted in real time to the operator’s automated workstation, allowing for timely decision making to prevent radioactive releases and improve environmental safety. The proposed method is a promising tool for ensuring reliable quality control of the fuel element cladding condition and improving nuclear and environmental safety. While the study is based on VVER-1000 reactor data, the flexibility of the proposed methodology suggests its potential applicability to other reactor types, opening avenues for broader implementation in diverse nuclear systems.

The results of numerous studies show that the control of power grid modes is carried out mainly using a technical criterion. The economic criterion is taken into account through the use of complex and inaccurate models that do not accurately predict the result. The emergence of market relations in the energy sector makes power systems economic entities in terms of production and satisfaction of demand for electricity by various economic entities (industry, households, businesses, etc.). Under these conditions, electricity is a commodity with a corresponding price and quality indicators. This requires the application of the risk assessment methodology as an economic category in the activities of power systems as a business entity. The methodology of risk assessment in market conditions requires business entities to search for methods to minimize risk as a possibility of adverse events. Under these conditions, it becomes possible to make the best management decisions regarding the most important criterion that reflects the interests of business entities at a given time. However, the imperfection of the relevant methodology for risk assessment in the energy sector delays their application in the industry. At the same time, when making management decisions, three possible levels can be distinguished: decision-making in conditions of certainty, when the result is presented in a deterministic form and can be determined in advance; decision-making under conditions of risk, when the outcome cannot be determined in advance, but there is information on the probability of distribution of possible consequences; decision-making in conditions where the outcome is random and there is no information about the consequences of the decision. An analysis of scientific publications shows that some authors’ works are devoted to solving the issues of applying the theory and principles of risks in the energy sector, in which the problem is solved only at the first two levels. At the same time, the operation of energy facilities is characterized by a high level of uncertainty and incomplete information about the consequences of such decisions. Therefore, the development of a methodology for making management decisions in the energy sector based on the theory and practice of risks, taking into account the high level of uncertainty and incomplete information, is an urgent scientific task. Implementation of algorithms and programs for controlling the modes of power grids based on them can meet the requirements for reliable and high-quality energy supply to the most demanding consumers and create favorable conditions for their business. This work is devoted to the development of scientific and methodological foundations for determining the voltage risk in power system networks, taking into account the uncertain nature of the loads and its impact on consumers. Based on the results of the study, a mathematical model of the risk of voltage collapses in networks, an algorithm and a methodology for its calculation were proposed.

Requirements of the international standard ISO 45001:2018 were analysed to identify the need for monitoring, measuring and analysing the functioning of the occupational health and safety management system. This analysis has made it clear that the effectiveness of the development and implementation of the occupational health and safety management system depends on the assessment methodology. The study focused on existing studies and publications on the assessment of processes, including those related to occupational safety, assessment methods or qualitative methods, and statistical methods used for assessment. As a result, the topic has been proven relevant, and the goal of the article was determined: to study the possibility of using qualimetric methods for evaluating the labour safety management system. A survey was conducted among workers at a machine-building enterprise to evaluate the occupational health and safety management system. Verbal scales were proposed to process the study results as they allow quantitative ratings to be obtained on the coded scale of the desirability function. The study result is a technique for obtaining a quantitative assessment of the occupational health and safety management system. This technique is universal and can be applied to any enterprise. It can also be used to make managerial decisions regarding the improvement of the occupational health and safety management system.

This study proposes a component-based model for assessing risks in the design of high-tech products. The model took into account the novelty of components, which affected the risk level in the development process. The risk assessment was based on fuzzy set theory, which allowed determination of the degree of importance of risk-generating factors, such as technical, economic, and organizational risks. The components were divided into “old” ones with the possibility of adaptation and “new” ones being implemented for the first time. The structure of the project included adaptation, acquisition, and development of new components. The component-oriented approach allowed for a reduction in the negative impact of risks in the early stages of development while optimizing decision-making on further product development. A case study involving the development of unmanned aerial vehicles (UAVs) was conducted to demonstrate the model’s applicability. The assessed aggregated project risk varied from 0.0992 for projects based primarily on reusable components to 0.1902 for those involving a high proportion of newly developed components. The model’s sensitivity to component novelty made it possible to differentiate between low- and moderate-risk design scenarios. This is especially valuable for early-stage project selection and risk-informed “go/no-go” decisions in the design of complex systems.

The study discusses approaches to assessing the quality of sustainable development indicators and analyses sustainable development indicators in general, for which the desirability function and the approach of translating sustainable development indicators into a dimensionless scale are used. This approach makes it possible to analyse the processes of achieving the sustainable development goals and relevant tasks on the basis of statistical data, as well as to compare indicators with different characteristics. For the purpose of qualimetric assessment, the article proposes to divide the indicators of sustainable development into four groups characterized by the following parameters: the lowest value is the best, the highest value is the best, the average value is the best, and the values that simultaneously tend to the lowest and the highest. It is proposed to evaluate sustainable development indicators in accordance with the group, taking into account the significance of the indicator, for which the form parameter and the evaluation step are selected by the expert evaluation method. For example, several sustainable development indicators for different groups are presented, and calculations are made to determine the dimensionless indicator, taking into account its significance according to the opinion of experts. As a result, we obtained dimensionless values for each of the sustainable development indicators (FQ = 0.92, 0.98, 0.86, 0.28, and 0.54), which characterize the achievement of sustainable development goals and allow us to assess progress in both a prospective and retrospective context.

In modern production systems, ensuring high product quality while minimising risk is a critical challenge. Traditional quality assessment methods often rely on expert judgment or complex models, which may introduce subjectivity or require large datasets. This study aims to develop a universal methodology for assessing product quality risks using a mathematically grounded approach that eliminates the need for expert-based evaluations and can be easily implemented in various industrial contexts. A qualimetric method based on nonlinear mathematical dependence using the error function “erf” is proposed. The method transforms measured quality indicators into a dimensionless scale and derives functionally dependent statistics under the assumption of a uniform distribution. The model is validated through analytical derivations and numerical experiments on piston components in precision mechanical engineering. A new mathematical model was established to calculate the probability density function of transformed quality indicators. The methodology enables the estimation of the probability that a quality indicator will fall within a risky range near tolerance limits. Numerical experiments confirmed the validity of the model, demonstrating its applicability to real-world production scenarios and its alignment with known principles of qualimetry. The proposed method provides a universal, objective, and practical tool for risk-based quality assessment. It can be applied across different industries, integrated into existing quality management systems, and used to support decision-making in production control. Future research should expand the model to accommodate nonuniform distributions and explore its integration with real-time quality monitoring systems.

Investment, the entry of foreign firms depends of a large extent on the country’s goodwill, which is reflected in various ratings. This representation of the situation is approximate, as it does not estimate the differences between the values of the indicators with adjacent grades. This can be avoided by dividing countries into homogeneous groups. It is appropriate to do so on the basis of non-linear grouping rather than linear grouping. It is based on the transformation of data into a dimensionless scale and linear grouping. In the case, its homogeneity increases thanks to the levelling of the most distinctive values and the alignment of the statistical characteristics of the groups. The aim of the article is to propose in principle, a new approach to the ranking of countries on the basis of their level of economic development. It was found that the nonlinear decision of countries into homogenous groups and compared to the linear grouping more accurately reflect the current situation.

The country's demographic situation reflects the role and potential of one of the most important factors of economic development, work, and therefore the quantitative assessment of the country's demographic profile is very important. In the recent period, the dominant in-depth but fragmentary studies of demographic issues do not allow to assess the situation in a complex way, integrating multidimensional and different demographic factors of different relevance, basic and dynamic. The purpose of this paper is to present a method of demographic profile assessment for complex analysis, based on a multicriteria method. This is usually done linearly, i.e., the relevance of the indicator does not depend on its value. In real life, this is not the case, so a nonlinear evaluation based on Harrington curves has been applied to the assessment of the demographic profile. The graphical-analytical method of trapezoids is applied to combine block values. In this case, the generalised value is the area under the curve, which is obtained by linearly connecting the dimensionless values of the indicators. The country's demographic profile index was obtained by combining the values of the basic and dynamic blocks in a respective way. In order to link the country's demographic profile index with GDP per capita, a correlation-regression analysis was performed, the results of which confirmed that the demographic status largely depends on the achieved level of economic development.

The article considers several modern scientific papers substantiating the need for assessing workplace safety and focusing on methods applied for the quantitative assessment of working conditions. The analysis found unsolved problems in qualimetry, which could lead to the development of new practical and generally applicable methods to effectively assess working conditions. The analysis proved the relevance of the topic and helped to determine the aim of the article, i.e., the development of a methodology for the quantitative assessment of working conditions in industries, considering harmful production factors. An exponential distribution, which belongs to the theory of extreme statistics, was proposed for the transition of heterogeneous single indicators of harmful factors into a dimensionless scale. Affine transformations were used to combine dissimilar scales, making it possible to divide segments on dissimilar scales into equal proportions. The article proposes a step-by-step method for determining a complex indicator of working conditions in industries. The proposed methodology allows management decisions that minimise the deviation in actual values of harmful factors from the optimal ones. The developed technique was tested at one specific metallurgical production site.

The European Union’s Green Deal emphasises the importance of improving the efficiency of the energy sector in its countries, which is why the issues involved are relevant in both scientific and practical terms. The article sets out the hypothesis that conveying the state of the economic efficiency of energy development by grades does not reflect the real situation. Instead of ranks, it is proposed to form homogeneous groups of some countries based on non-linear data normalisation instead of today’s universally used linearisation. Grouping the euro area countries in the European Union on the basis of the value of the cost-effectiveness indicator for the energy development of their industrial sector confirmed the appropriateness of the proposed method-ology. In this way, three groups of countries were formed according to the level of cost-effectiveness achieved. The proposed methodology for grouping countries is universal and can be used for international comparisons of any kind.